\newproblem{lay:6_1_28}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 6.1.28}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Suppose $\mathbf{y}$ is orthogonal to $\mathbf{u}$ and $\mathbf{v}$. Show that $\mathbf{y}$ is orthogonal to every $\mathbf{w}$ in $\mathrm{Span}\{\mathbf{u},\mathbf{v}\}$.
	[\textit{Hint}: An arbitrary $\mathbf{w}$ in $\mathrm{Span}\{\mathbf{u},\mathbf{v}\}$ has the form $\mathbf{w}=c_1\mathbf{u}+c_2\mathbf{v}$.]
}{
   % Solution
	Let us calculate the inner product between $\mathbf{y}$ and $\mathbf{w}$
	\begin{center}
		$\begin{array}{rcl}
			\mathbf{y}\cdot\mathbf{w}&=&\mathbf{y}\cdot(c_1\mathbf{u}+c_2\mathbf{v})\\
			   &=&c_1\mathbf{y}\cdot\mathbf{u}+c_2\mathbf{y}\cdot\mathbf{v}\\
				 &=&c_1\cdot 0+c_2\cdot 0\\
				 &=&0
		\end{array}$
	\end{center}
	where we have made used of the fact that $\mathbf{y}$ is orthogonal to $\mathbf{u}$ and $\mathbf{v}$, that is, $\mathbf{y}\cdot\mathbf{u}=\mathbf{y}\cdot\mathbf{v}=0$.
}
\useproblem{lay:6_1_28}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
